Beyond Expansion II: Low-Lying Fundamental Geodesics
Number Theory
2016-06-22 v2 Dynamical Systems
Abstract
A closed geodesic on the modular surface is "low-lying" if it does not travel "high" into the cusp. It is "fundamental" if it corresponds to an element in the class group of a real quadratic field. We prove the existence of infinitely many low-lying fundamental geodesics, answering a question of Einsiedler-Lindenstrauss-Michel-Venkatesh.
Cite
@article{arxiv.1406.1366,
title = {Beyond Expansion II: Low-Lying Fundamental Geodesics},
author = {Jean Bourgain and Alex Kontorovich},
journal= {arXiv preprint arXiv:1406.1366},
year = {2016}
}
Comments
39 pages, 1 figure. This paper is a complete re-write of the posting arXiv:1310.7190, making the latter obsolete. The main tools are similar, but the application is in some sense orthogonal to the initial goal. We hope to return to the questions of the earlier paper at a later date